system of distinct representatives

Let $S=\{S_1,S_2,\mathrm{\dots }{S}_n\}$ be a finite collection of finite sets. A system of distinct representatives, or SDR, of $S$ is a set

$$x_1\in S_1,x_2\in S_2,\mathrm{\dots }{x}_n\in S_n$$

such that

$$x_i\ne x_j\text{ whenever }i\ne j$$

(i.e., each choice must be unique).

Title	system of distinct representatives
Canonical name	SystemOfDistinctRepresentatives
Date of creation	2013-03-22 12:35:11
Last modified on	2013-03-22 12:35:11
Owner	vampyr (22)
Last modified by	vampyr (22)
Numerical id	4
Author	vampyr (22)
Entry type	Definition
Classification	msc 05D15
Synonym	SDR